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Two-loop scale dependence of the static QCD potential including quark masses

Brodsky, Stanley J. ; Melles, Michael and Rathsman, Johan LU (1999) In Physical Review D 60(9).
Abstract

The interaction potential V(Q2) between static test charges can be used to define an effective charge αv(Q2) and a physically based renormalization scheme for quantum chromodynamics and other gauge theories. In this paper we use recent results for finite-mass fermionic corrections to the heavy-quark potential at two loops to derive the next-to-Ieading order term for the Gell-Mann-Low function of the V scheme. The resulting effective number of flavors NF(Q2/m2) in the αv scheme is determined as a gauge-independent and analytic function of the ratio of the momentum transfer to the quark pole mass. The results give an automatic decoupling of heavy quarks and are... (More)

The interaction potential V(Q2) between static test charges can be used to define an effective charge αv(Q2) and a physically based renormalization scheme for quantum chromodynamics and other gauge theories. In this paper we use recent results for finite-mass fermionic corrections to the heavy-quark potential at two loops to derive the next-to-Ieading order term for the Gell-Mann-Low function of the V scheme. The resulting effective number of flavors NF(Q2/m2) in the αv scheme is determined as a gauge-independent and analytic function of the ratio of the momentum transfer to the quark pole mass. The results give an automatic decoupling of heavy quarks and are independent of the renormalization procedure. Commensurate scale relations then provide the next-to-leading order connection between all perturbatively calculable observables to the analytic and gaugeinvariant av scheme without any scale ambiguity and a well-defined number of active flavors. The inclusion of finite quark mass effects in the running of the coupling is compared with the standard treatment of finite quark mass effects in the minimal subtraction (MS) scheme.

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author
; and
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review D
volume
60
issue
9
article number
096006
publisher
American Physical Society
external identifiers
  • scopus:33750226431
ISSN
0556-2821
DOI
10.1103/PhysRevD.60.096006
language
English
LU publication?
no
id
b81a0fa4-365a-4910-a5d7-6eaa596bbe91
date added to LUP
2019-05-14 13:49:39
date last changed
2022-01-31 19:50:26
@article{b81a0fa4-365a-4910-a5d7-6eaa596bbe91,
  abstract     = {{<p>The interaction potential V(Q<sup>2</sup>) between static test charges can be used to define an effective charge α<sub>v</sub>(Q<sup>2</sup>) and a physically based renormalization scheme for quantum chromodynamics and other gauge theories. In this paper we use recent results for finite-mass fermionic corrections to the heavy-quark potential at two loops to derive the next-to-Ieading order term for the Gell-Mann-Low function of the V scheme. The resulting effective number of flavors N<sub>F</sub>(Q<sup>2</sup>/m<sup>2</sup>) in the α<sub>v</sub> scheme is determined as a gauge-independent and analytic function of the ratio of the momentum transfer to the quark pole mass. The results give an automatic decoupling of heavy quarks and are independent of the renormalization procedure. Commensurate scale relations then provide the next-to-leading order connection between all perturbatively calculable observables to the analytic and gaugeinvariant av scheme without any scale ambiguity and a well-defined number of active flavors. The inclusion of finite quark mass effects in the running of the coupling is compared with the standard treatment of finite quark mass effects in the minimal subtraction (MS) scheme.</p>}},
  author       = {{Brodsky, Stanley J. and Melles, Michael and Rathsman, Johan}},
  issn         = {{0556-2821}},
  language     = {{eng}},
  month        = {{12}},
  number       = {{9}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review D}},
  title        = {{Two-loop scale dependence of the static QCD potential including quark masses}},
  url          = {{http://dx.doi.org/10.1103/PhysRevD.60.096006}},
  doi          = {{10.1103/PhysRevD.60.096006}},
  volume       = {{60}},
  year         = {{1999}},
}